Car park layout - what is good, what is best?

The magazine of the Institute of Mathematics and its Applications (Mathematics Today, August 2015) has an interesting and amusing article about optimising the layout of car parking spaces in a car park. Tina and I have found several car parks at supermarkets and motorway services where the layout of spaces strikes us as sub-optimal. (Mind you, the way that drivers negotiate such car parks is also sub-optimal.)

So, what does the article consider? It focuses on those which are on one level, not multi-storey. Most car parks have a rectangular pattern with corridors for cars, and parking spaces at right angles, creating a rectangular pattern. What happens if you have the spaces at an angle, creating a herringbone pattern? Or if alternate corridors have traffic moving in opposite directions, so you can have a diagonal pattern? The corridors can be narrower, because cars do not need so much space to turn. So, you can have more corridors. But possibly fewer spaces per corridor.

This problem has been examined in more detail by mathematicians atBristol University(report here)

In Mathematics Today, the problem is treated as an optimisation problem with the fixed parameters length of bay, width of bay and turning circle of car, and one decision - the angle of the bay. The car park is assumed to be infinite (as some car parks appear to be). Taking the fixed parameters of a Rolls Royce Phantom, the best angle is about 36 degrees - but the optimal solution is insensitive to small changes so one could suggest either 30 or 45 (easier to measure).

Car users are very conservative, so it is unlikely that many car park designers will change to increase the capacity of their creations in this way. But there is scope for designers to think about the likely flow of vehicles to try and achieve designs which are efficient and work.

For a completely whimsical discussion about the possibilities of an irregular layout of markings on a car park, Ian Stewart's book "Another Fine Math You've Got Me Into" has a chapter (The Thermodynamics of Curlicues) where the author imagines someone laying out a car park following Dekking and Mendes-France curves.